Rewrite as a simplified fraction. ${3.49\overline{1} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3491.1111...\\ 100x &= 349.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3142}$ ${x = \dfrac{3142}{900}} $ ${x = \dfrac{1571}{450}} \text{or} {3 \dfrac{221}{450}}$